Abstract
In this work the modulus of continuity of functions in the Lp metric (1 ≤ p < ∞) is estimated through its best approximations in this metric by Haar and Walsh polynomials. Besides, estimates of best approximations of functions by Haar and Walsh polynomials in the Lq metric are obtained by the same approximations in the Lp metric (1 ≤ p ≤ ∞). In the last case, the results are analogous to those which were proved for approximations by trigonometric polynomials by P. L. Ul'janov and also by S. B. Steckin and A. A. Konjuskov. Bibliography: 26 items.
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